# Relativistic momentum is 1% greater than classical, at what speed?

## Homework Statement

How fast must a body be traveling if its forrect relativistic momentum is 1% greater than the classical momentum

## Homework Equations

P_r = mv/sqrt(1-(v^2/c^2))
P_nr = mv
p_r = 1.01P_nr

## The Attempt at a Solution

mv/sqrt(1-(v^2/c^2)) = 1.01mv
mv = 1.01(mv)[sqrt(1-(v^2/c^2))]
1 = 1.01[sqrt(1-(v^2/c^2))]
1/1.01 = sqrt(1-(v^2/c^2))
(1/1.01)^2 = 1-(v^2/c^2)
0.980296 = 1-(v^2/c^2)
0.980296 - 1 = -(v^2/c^2)
-0.01970 = -(v^2/c^2)
(-0.01970)(c^2) = -v^2
0.01970c^2 = v^2
0.0003884c = v

However, this is not the correct answer. The actual answer in the back of the textbook is 0.14c. If anyone can correct my algebra or point me into the right direction it would be greatly appreciated.

Thanks

## Answers and Replies

gabbagabbahey
Homework Helper
Gold Member
0.01970c^2 = v^2
0.0003884c = v

The square root of 0.01970 is not 0.0003884 I cannot believe I overlooked that, it turned out I was squaring the 0.01970. Thanks a lot :)